The angle between two unit vectors and is and  .

Which of the following best describes the possible range of values of  ?

Consider the vectors    and  .

Given that    is the angle between    and  ,  and    is the angle between    and    is

For the two vectors    and    it is know that

Which of the following statements MUST be true?

1. Either,   is negative and    is positive, or    is positive and    is negative.
2. The angle between    and    is obtuse.
3. The product    is negative.
4. The points , and are collinear.

Using vectors, calculate the acute angle between the line that passes through    and    and the line that passes through    and  .

Give your answer correct to one decimal place.  (2 marks)

What is the angle between the vectors    and  ?

A.   

B.   

C.   

D.   

If    is the angle between    and  , then find the exact value of  .  (2 marks)

Relative to a fixed origin, the points , and are defined respectively by the position vectors    and  , where    is a real constant.

If the magnitude of angle   is  , find .  (3 marks)

Points    and    have position vectors    and  respectively.

Find the angle between    and    to the nearest minute.  (2 marks)

Consider the vectors given by    and  , where  .

Find the value(s) of    if the acute angle between    and    is 30°.   (2 marks)